1. Field of the Invention
The invention relates to a flow duct for the passage of a two-phase flow which has a liquid and a gaseous phase, comprising an inner wall completely enclosing the two-phase flow radially to the direction of flow.
2. Discussion of Background
Two-phase flows are mass flows which are composed of two different flows of substances, for example a mixture of a liquid and a gas. Such two-phase flows are important, for example, in the compression of air which is fed in compressed form to an energy-generating plant. Thus ideas are known which utilize the principle of isothermal compression for the supply of gas-turbine plants with precompressed air, as disclosed, for example, by US publication U.S. Pat No. 4,797,563.
In the case described above, an air/water mixture is accelerated along an incline and then directed into a pressure chamber. Further developments in this respect provide for the accelerated two-phase flow to be directed for the purposes of compression into a nozzle arrangement, for example into a Laval nozzle, within which kinetic energy is specifically extracted from the two-phase mixture, while at the same time the air contained in the mixture is compressed. It has been possible to show that the selection of the droplet size of the water drops contained in the water/air mixture has a decisive effect on the efficiency of the nozzle with regard to its compression characteristics.
However, more extensive investigations with regard to the flow-duct wall enclosing the two-phase flow have not been carried out so far. In particular, more accurate knowledge of the boundary-layer behavior between the two-phase flow and the flow-duct wall could in this case make a decisive contribution to improvements with regard to the avoidance of flow losses on account of friction as well as the occurrence of phase separations, as a result of which the efficiency of a flow duct, in particular of a two-phase Laval nozzle, could be considerably improved.
A few interesting aspects of the flow behavior of a two-phase flow through a flow duct may be gathered from the following contributions:
I. M. R. Wang and D. Y. Huang, Droplet dispersion and ejection process in two-phase boundary layer, AIAA Journal 32 (11), 2217 (1994). PA1 II. Y. Tsuji and Y. Morikawa, LDV measurements of an air-solid two-phase flow in a horizontal pipe, J. Fluid Mech. 120, 385 (1982). PA1 III. Y. Tsuji, Y. Morikawa and H. Shiomi, LDV measurements of an air-solid two-phase flow in a vertical pipe, J. Fluid Mech. 139, 417 (1984).
It can be gathered from the contribution from Wang and Huang that the momentum exchange between a flow and a wall surrounding the flow may be increased provided the flow contains droplets. In this case, it is noteworthy that the droplet density within the boundary layer directed toward the wall surface decreases linearly to the value 0, irrespective of the size of the respective droplets present in the flow. Thus it is also noteworthy that an aerosol having a water/air mixture ratio of about 0.005 causes approximately twice the wall shearing force than is the case with a boundary layer which consists of pure air. Thus the aforesaid contributions from Tsuji and Morikawa also confirm an existing proportionality between the increase in the wall shearing force of a mass flow along a wall and the water/air mass ratio. It is in principle the case that the boundary layer forming along a wall becomes richer in water droplets with an increasing water/air mass ratio within the mass flow flowing through the flow duct.
The momentum transfer to the wall over which a mass flow flows essentially determines the tendency of a two-phase flow to separate into two different phases, at least in the region of the boundary layer.
In particular when a two-phase flow flows through a Laval nozzle, which produces a large pressure gradient within the flow in the direction of flow, a phase separation is undesirable, so that the momentum transfer to the wall has to be designed to be sufficiently small. On the other hand, a very high momentum transfer and, associated therewith, a high wall shearing force contributes to energy losses within the mass flow flowing through the nozzle arrangement, this mass flow considerably reducing the efficiency of the Laval nozzle.